The invention relates to a method of machining round material or the like by the whirling process. The whirling process consists of clamping a workpiece for machining into a whirling unit. The workpiece is held stationary with regard to its longitudinal center axis. A whirling annular cutting tool having an internal tooth system is traversable on a compound slide. The tool is movable in a perpendicular plane relative to the longitudinal center axis of the workpiece. Cutting movement of the tool occurs as a result of a displacement of the tool's flight-circle center point on a flight-circle center point path.